its easiest to take the bike with you when you fly. for international flights its included in the 2 pieces of luggage you are allowed. if you are going to take 3 pieces of luggage i would still fly with the bike as its much cheaper than shipping it by far.
i would recommend a cardboard box that you can dispose of and simply pick up another from a bike shop before you return. but if you do a google search for local bike shops in the area i am sure they will put up with your box for that time. or ask a hostel or hotel. NZ is a very friendly place!